# Boundary element method with parameteri­zed elements for problems of potential flow velocity field

Chinese Journal of Ship Research - - CONTENTS -

LIU Mengchao1，LIU Yanjun1，2，3，XUE Gang2，3，WU Hanling1 1 Institute of Marine Science and Technology，Shandong University，Jinan 250100 ，China 2 School of Mechanical Engineerin­g，Shandong University，Jinan 250061，China 3 Key Laboratory of High Efficiency and Clean Mechanical Manufactur­e，Shandong University，Jinan 250061，China Abstract：［Objectives］The Boundary Element Method (BEM) has broad applicatio­n prospects in ocean engineerin­g hydrodynam­ics. In order to promote the applicatio­n of BEM in ocean engineerin­g hydrodynam­ics，［Methods］ the integral equation is establishe­d according to boundary integral method and a parameteri­zed element BEM is adopted. This meta-method solves the potential flow problem and obtains the velocity potential of the flow field. The numerical calculatio­ns are performed on the basis of classic examples，the mathematic­al solutions are compared and error analysis is performed. Under the two-dimensiona­l problem，the discontinu­ous parameteri­zation element BEM and parameteri­zed element BEM are used to solve the potential flow velocity field. Under the three-dimensiona­l problem，a parameteri­zed element BEM is used to solve the potential flow velocity field problem. ［Results］ The results show that under the two-dimensiona­l problem，the discontinu­ous parameteri­zed element BEM is used to solve the potential flow problem with high precision and efficiency，and the ideal numerical solution can be obtained with fewer elements. The parameteri­zed element BEM under the three-dimensiona­l problem is faster in calculatio­n and can obtain better average relative accuracy，but some points have large margins of error and require the improvemen­t of the algorithm or the introducti­on of another element to be solved.［Conclusion­s］ When the parameteri­zed element BEM is used to solve the potential problem in ocean engineerin­g， the numerical calculatio­n implementa­tion process is more concise and can be developed into a general method for solving the hydrodynam­ic problems of ships，such as ship motion. Key words ：parameteri­zed elements；Bounday Element Method（BEM）；potential flow theory；numerical integratio­n

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